A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science

2010 ◽  
Vol 3 (4) ◽  
pp. 1015-1046 ◽  
Author(s):  
Ernie Esser ◽  
Xiaoqun Zhang ◽  
Tony F. Chan
Keyword(s):  
Convex Optimization ◽  
General Framework ◽  
First Order ◽  
Imaging Science ◽  
Primal Dual

scholarly journals A Preconditioning Technique for First-Order Primal-Dual Splitting Method in Convex Optimization

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Meng Wen ◽  
Jigen Peng ◽  
Yuchao Tang ◽  
Chuanxi Zhu ◽  
Shigang Yue
Keyword(s):  
Iterative Algorithm ◽  
General Framework ◽  
Optimization Problems ◽  
Splitting Method ◽  
Iteration Process ◽  
First Order ◽  
Preconditioning Technique ◽  
Primal Dual ◽  
Preconditioned Iterative ◽  
Better Than

We introduce a preconditioning technique for the first-order primal-dual splitting method. The primal-dual splitting method offers a very general framework for solving a large class of optimization problems arising in image processing. The key idea of the preconditioning technique is that the constant iterative parameters are updated self-adaptively in the iteration process. We also give a simple and easy way to choose the diagonal preconditioners while the convergence of the iterative algorithm is maintained. The efficiency of the proposed method is demonstrated on an image denoising problem. Numerical results show that the preconditioned iterative algorithm performs better than the original one.

scholarly journals An Implementable First-Order Primal-Dual Algorithm for Structured Convex Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Feng Ma ◽  
Mingfang Ni ◽  
Lei Zhu ◽  
Zhanke Yu
Keyword(s):  
Convex Optimization ◽  
Practical Interest ◽  
Principal Component ◽  
Objective Functions ◽  
Dual Algorithm ◽  
Proximal Point ◽  
Pursuit Problem ◽  
First Order ◽  
Structured Convex Optimization ◽  
Primal Dual

Many application problems of practical interest can be posed as structured convex optimization models. In this paper, we study a new first-order primaldual algorithm. The method can be easily implementable, provided that the resolvent operators of the component objective functions are simple to evaluate. We show that the proposed method can be interpreted as a proximal point algorithm with a customized metric proximal parameter. Convergence property is established under the analytic contraction framework. Finally, we verify the efficiency of the algorithm by solving the stable principal component pursuit problem.

scholarly journals A General Framework for Decentralized Optimization With First-Order Methods

2020 ◽  
Vol 108 (11) ◽  
pp. 1869-1889
Author(s):  
Ran Xin ◽  
Shi Pu ◽  
Angelia Nedic ◽  
Usman A. Khan
Keyword(s):  
General Framework ◽  
Decentralized Optimization ◽  
First Order ◽  
First Order Methods

First-order methods of smooth convex optimization with inexact oracle

2013 ◽  
Vol 146 (1-2) ◽  
pp. 37-75 ◽  
Author(s):  
Olivier Devolder ◽  
François Glineur ◽  
Yurii Nesterov
Keyword(s):  
Convex Optimization ◽  
Smooth Convex ◽  
First Order ◽  
Inexact Oracle ◽  
Smooth Convex Optimization ◽  
First Order Methods

scholarly journals First-Order Methods for Convex Optimization

2021 ◽  
pp. 100015
Author(s):  
Pavel Dvurechensky ◽  
Shimrit Shtern ◽  
Mathias Staudigl
Keyword(s):  
Convex Optimization ◽  
First Order ◽  
First Order Methods
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